In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved directly by substituting the displacement fields with equivalent finite double Chebyshev polynomials. Using this method allows one to analyze the composite laminated plates with combination of different boundary conditions on all edges. The final nonlinear system of equations is obtained by discretizing both equilibrium equations and boundary conditions with finite Chebyshev polynomials. Nonlinear terms caused by the product of variables are linearized by using quadratic extrapolation technique to solve the system of equations. Since number of equations is always more than the number of unknown parameters, the least squares technique is used to solve the system of equations. Some results for angle-ply and cross-ply composite plates with different boundary conditions are computed and compared with those available in the literature, wherever possible.